Sign of the color-hyperfine splitting in charmonium P states as a test of perturbative QCD

The sign of the difference in energy between the center of gravity of the {sup 3}{ital P} levels and the {sup 1}{ital P} level in heavy quarkonium is a test of the {alpha}{sub {ital s}}{sup 2} terms in perturbative QCD with a fixed coupling constant. Whereas this energy difference is zero in the Fer...

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Bibliographic Details
Published in:Physical review. D, Particles and fields Particles and fields, 1992-05, Vol.45 (9), p.3268-3271
Main Authors: LICHTENBERG, D. B, PREDAZZI, E, RONCAGLIA, R
Format: Article
Language:English
Subjects:
662230 - Quantum Chromodynamics- (1992-)
662240 - Models for Strong Interactions- (1992-)
662440 - Properties of Other Particles Including Hypothetical Particles- (1992-)
ANGULAR MOMENTUM
BOSONS
BOTTOMONIUM
CHARMONIUM
Classical and quantum physics: mechanics and fields
COLOR MODEL
COMPOSITE MODELS
COULOMB FIELD
COUPLING CONSTANTS
ELECTRIC FIELDS
ELECTRODYNAMICS
ELEMENTARY PARTICLES
ENERGY LEVELS
Exact sciences and technology
FERMIONS
FIELD THEORIES
HADRONS
HYPERFINE STRUCTURE
MATHEMATICAL MODELS
MESONS
P STATES
PARTICLE MODELS
PARTICLE PROPERTIES
PERTURBATION THEORY
Physics
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
POSTULATED PARTICLES
QUANTUM CHROMODYNAMICS
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
QUARK MODEL
QUARKONIUM
QUARKS
SPIN
TESTING
Theory of quantized fields
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Summary:The sign of the difference in energy between the center of gravity of the {sup 3}{ital P} levels and the {sup 1}{ital P} level in heavy quarkonium is a test of the {alpha}{sub {ital s}}{sup 2} terms in perturbative QCD with a fixed coupling constant. Whereas this energy difference is zero in the Fermi-Breit approximation and greater than zero in a generalized Fermi-Breit approximation with asymptotically free potentials, the energy difference is negative in perturbative QCD calculations to one-loop order with a fixed {alpha}{sub {ital s}}. For potentials which reasonably agree with the spin-averaged data, the absolute magnitude of the splitting is calculated to be about 4 MeV or less in charmonium and 2 MeV or less in bottomonium. Since the energy of the {sup 3}{ital P} center of gravity in charmonium is known, a measurement of the energy of the {sup 1}{ital P} level is needed to discriminate between these different schemes. Although the {sup 1}{ital P} levels in bottomonium will probably be harder to measure, we also present results for bottomonium.
ISSN:0556-2821
1089-4918
DOI:10.1103/PhysRevD.45.3268